Metamagnetic Quantum Criticality in Sr3Ru2O7

  • A. J. Schofield
  • A. J. Millis
  • S. A. Grigera
  • G. G. Lonzarich
Part of the Lecture Notes in Physics book series (LNP, volume 603)


We consider the metamagnetic transition in the bilayer ruthenate, Sr3Ru2O7, and use this to motivate a renormalization group treatment of a zero-temperature quantum-critical end-point. We summarize the results of mean field theory and give a pedagogical derivation of the renormalization-group equations. These are then solved to yield numerical results for the susceptibility, the specific heat and the resistivity exponent which can be compared with measured data on Sr3Ru2O7 to provide a powerful test for the standard framework of metallic quantum criticality. The observed approach to the critical point is well-described by our theory explaining a number of unusual features of experimental data. The puzzling behaviour very near to the critical point itself, though, is not accounted for by this, or any other theory with a Fermi surface.


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  1. 1.
    A.P. Mackenzie, S.R. Julian, A.J. Diver, G.J. McMullan, M.P. Ray, G.G. Lonzarich, Y. Maeno, S. Nishizaki, T. Fujita: Phys. Rev. Lett. 76, 3786 (1996)CrossRefADSGoogle Scholar
  2. 2.
    Y. Maeno, H. Hashimoto, K. Yoshida, S. Nishizaki, T. Fujita, J.G. Bednorz, F. Lichtenberg: Nature 372, 532 (1994)CrossRefADSGoogle Scholar
  3. 3.
    T. M. Rice: Nature 396, 627 (1998)CrossRefADSGoogle Scholar
  4. 4.
    R.S. Perry, L.M. Galvin, S.A. Grigera, L. Capogna, A.J. Schofield, A.P. Mackenzie, M. Chiao, S. R. Julian, S.I. Ikeda, S. Nakatsuji, Y. Maeno, C. Pfleiderer: Phys. Rev. Lett. 86, 2661 (2001)CrossRefADSGoogle Scholar
  5. 5.
    S.A. Grigera, R.S. Perry, A.J. Schofield, M. Chiao, S.R. Julian, G.G. Lonzarich, S.I. Ikeda, Y. Maeno, A.J. Millis, A. P. Mackenzie: Science 294, 329 (2001)CrossRefADSGoogle Scholar
  6. 6.
    J. A. Hertz: Phys. Rev. B 14, 1165 (1976)CrossRefADSGoogle Scholar
  7. 7.
    A. J. Millis: Phys. Rev. B 48, 7183 (1993)CrossRefADSGoogle Scholar
  8. 8.
    M.B. Suvasini, G.Y. Guo, W.M. Temmerman, G.A. Gehring: Phys. Rev. Lett. 71, 2983 (1993)CrossRefADSGoogle Scholar
  9. 9.
    P. Haen, J. Flouquet, F. Lapierre, P. Lejay, G. Remenyi: J. Low Temp. Phys. 67, 391 (1987)CrossRefADSGoogle Scholar
  10. 10.
    H. Aoki, S. Uji, A. K. Albessard, Y. Onuki: Phys. Rev. Lett. 71, 2110 (1993)CrossRefADSGoogle Scholar
  11. 11.
    J. Flouquet, S. Kambe, L. P. Regnault, P. Haen, J.P. Brison, F. Lapierre, P. Lajey: Physica B 215, 77 (1995)CrossRefADSGoogle Scholar
  12. 12.
    T. Hamamoto, K. Kindo, T.C. Kobayashi, Y. Uwatoko, S. Araki, R. Settai, Y. Onuki: Physica B 281–282, 64 (2000)CrossRefGoogle Scholar
  13. 13.
    See, e.g. articles in Proceedings of the 6th International Conference on Research in High Magnetic Fields, published in Physica B 94–5, (2001) or in the SCES98 proceedings, Physica B 259–261, (1999)Google Scholar
  14. 14.
    C. Thessieu, C. Pfleiderer, A.N. Stepanov, J. Flouquet: J. Phys.: Cond. Matter 9,6677 (1997)CrossRefADSGoogle Scholar
  15. 15.
    S. Ikeda, Y. Maeno, M. Kosaka, Y. Uwatoko: Phys. Rev. B 62, R6089 (2000)CrossRefADSGoogle Scholar
  16. 16.
    D.J. Singh, I.I. Mazin: Phys. Rev. B, 63, 165101 (2001)CrossRefADSGoogle Scholar
  17. 17.
    S.R. Julian, C. Pfleiderer, F.M. Grosche, N.D. Mathur, G.J. McMullan, A.J. Diver, I.R. Walker, G.G. Lonzarich: J. Phys.: Cond. Matter 8, 9675 (1996)CrossRefADSGoogle Scholar
  18. 18.
    Hilbert von Löhneysen: J. Phys.: Cond. Matter 8, 9689 (1996)CrossRefADSGoogle Scholar
  19. 19.
    S. Chakravarty, R.B. Laughlin, D.K. Morr, C. Nayak: Phys. Rev. B 63, 094503 (2001)CrossRefADSGoogle Scholar
  20. 20.
    P. Gegenwart, F. Kromer, M. Lang, G. Sparn, C. Geibel, F. Steglich: Phys. Rev. Lett. 82, 1293 (1999)CrossRefADSGoogle Scholar
  21. 21.
    A. Schröder, G. Aeppli, R. Coldea, M. Adams, O. Stockert, H. v. Löhneysen, E. Bucher, R. Ramazashvili, P. Coleman: Nature 407, 351 (2000)CrossRefADSGoogle Scholar
  22. 22.
    P. Coleman, C. Pepin, Q. Si, R. Ramazashvili: J. Phys.: Cond. Matter 13, R723 (2001)CrossRefADSGoogle Scholar
  23. 23.
    D. Belitz, T.R. Kirkpatrick, Thomas Vojta: Phys. Rev. B 65, 165112 (2002)CrossRefADSGoogle Scholar
  24. 24.
    A. Rosch: Phys. Rev. Lett. 82, 4280 (1999)CrossRefADSGoogle Scholar
  25. 25.
    D. Meyer, W. Nolting: Phys. Rev. B 64, 052404 (2001)CrossRefADSGoogle Scholar
  26. 26.
    H. Satoh, F.J. Ohkawa: Phys. Rev. B 63, 184401 (2001)CrossRefADSGoogle Scholar
  27. 27.
    H. Yamada: Phys. Rev. B 47, 11211 (1993)CrossRefADSGoogle Scholar
  28. 28.
    H. Yamada, K. Terao: Phys. Rev. B 59, 9342 (1999)CrossRefADSGoogle Scholar
  29. 29.
    A.J. Millis, A.J. Schofield, G.G. Lonzarich, S.A. Grigera: Phys. Rev. Lett. 88, 217204 (2002)CrossRefADSGoogle Scholar
  30. 30.
    J.W. Negele, H. Orland: Quantum many-particle systems, (Addison-Wesley Publishing Company, Inc., 1987)Google Scholar
  31. 31.
    E.C. Stoner: Rep. Prog. Phys. 11, 43 (1947)CrossRefADSGoogle Scholar
  32. 32.
    D. Belitz, T.R. Kirkpatrick, T. Vojta: Phys. Rev. B, 55 9452, 1997.CrossRefADSGoogle Scholar
  33. 33.
    G.Y. Chitov, A.J. Millis: Phys. Rev. Lett. 86, 5337 (2001)CrossRefADSGoogle Scholar
  34. 34.
    E.I. Blount: Phys. Rev. B, 32:2935 (1985)CrossRefADSGoogle Scholar
  35. 35.
    L. Capogna, E.M. Forgan, S.M. Hayden, A. Wildes, J.A. Duffy, A.P. Mackenzie, R.S. Perry, S. Ikeda, Y. Maeno, S.P. Brown: cond-mat/0201556Google Scholar
  36. 36.
    D. Belitz, T.R. Kirkpatrick, A.J. Millis, T. Vojta Phys. Rev. B: 58:14155, (1998)CrossRefADSGoogle Scholar
  37. 37.
    G. Busiello, L. De Cesare, I. Rabuffo: Phys. Rev. B 29, 4189 (1984)CrossRefADSGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2002

Authors and Affiliations

  • A. J. Schofield
    • 1
  • A. J. Millis
    • 2
  • S. A. Grigera
    • 3
  • G. G. Lonzarich
    • 4
  1. 1.School of Physics and AstronomyUniversity of BirminghamEdgbastonUK
  2. 2.Department of PhysicsColumbia UniversityNew YorkUSA
  3. 3.School of Physics and AstronomyUniversity of St. AndrewsSt AndrewsUK
  4. 4.Cavendish LaboratoryCambridgeUK

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